Disjoint Union (topology) - Preservation of Topological Properties

Preservation of Topological Properties

  • every disjoint union of discrete spaces is discrete
  • Separation
    • every disjoint union of T0 spaces is T0
    • every disjoint union of T1 spaces is T1
    • every disjoint union of Hausdorff spaces is Hausdorff
  • Connectedness
    • the disjoint union of two or more nonempty topological spaces is disconnected

Read more about this topic:  Disjoint Union (topology)

Famous quotes containing the words preservation of, preservation and/or properties:

    There is something to be said for jealousy, because it only designs the preservation of some good which we either have or think we have a right to. But envy is a raging madness that cannot bear the wealth or fortune of others.
    François, Duc De La Rochefoucauld (1613–1680)

    I do seriously believe that if we can measure among the States the benefits resulting from the preservation of the Union, the rebellious States have the larger share. It destroyed an institution that was their destruction. It opened the way for a commercial life that, if they will only embrace it and face the light, means to them a development that shall rival the best attainments of the greatest of our States.
    Benjamin Harrison (1833–1901)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)